Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

Spatial Pre-Coding for Multi-Carrier Transmission 323FSPCΛChannelEstimationRx antennaIOFDMSymbolDemapperChannelDecoderFigure 6-26Receiver of an OFDM system with spatial pre-coding with a single Rx antennaThe channels from the two transmit antennas to the receive antenna are given by thecomplex-valued fading coefficients H n (1) and H n(2) respectively. The superimposed channelat the receiver antenna isH n = H n (1) + H n (2) . (6.22)The block diagram of the receiver is shown in Figure 6-26. The receiver can have multiplereceive antennas. For simplification but without loss of generality, the case with onereceiver antenna is analyzed in the following. At the receiver antenna, the signals fromthe different transmit antennas superimpose. Depending on the spatial pre-coding scheme,the receiver has to estimate all channels from the M transmit antennas to the receiverantenna or only the superimposed channel coefficient H n .The spatial pre-coding schemes are presented with increasing complexity, i.e. spatialphase coding (SPC), selection diversity (SD), equal gain transmission (EGT), and maximumratio transmission (MRT) [13, 16, 18, 22]. The least complex pre-coding scheme isSPC, which requires only the estimation of the superimposed channel H n at the receiveranda1bitfeedbackF . The most complex is MRT, which requires the estimation of thechannels from each transmit antenna to the receive antenna and a feedback that providesthis information to the transmitter.6.4.1 Spatial Phase Coding (SPC)The principle of SPC is to achieve a constructive superposition of the signals from thedifferent transmit antennas at the receiver antenna without the necessity to estimate thetwo channels from the two transmit antennas to the receive antenna. Only one channelhas to be estimated, which is the superimposed channel H n .By comparing the absolute value of the superimposed channel |H n | with a predefinedthreshold , SPC can detect a destructive superposition at the receiver with high probabilityand indicates to the transmitter over a feedback channel that the phase relation ofthe transmitted signals should in this case be changed by π. A straightforward solution isto flip the phase of the signal at one transmit antenna by π. Thus in the subsequent transmissionthe channels superimpose constructively at the receive antenna. The assumptionis that the phase relation between both channels is quasi constant between subsequenttransmissions. This is a typical assumption in OFDM systems. If due to variations of thechannel over the time |H n | falls below the threshold again, the phase will be flippedagain.The spatial phase encoder has two possible states. These are termed state A and stateB. Depending on the actual state, the data symbols s n to be transmitted are pre-coded in